The sum of two numbers is $88$, and their difference is $62$. What are the two numbers?
Explanation: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 88}$ ${x-y = 62}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 150 $ $ x = \dfrac{150}{2} $ ${x = 75}$ Now that you know ${x = 75}$ , plug it back into $ {x+y = 88}$ to find $y$ ${(75)}{ + y = 88}$ ${y = 13}$ You can also plug ${x = 75}$ into $ {x-y = 62}$ and get the same answer for $y$ ${(75)}{ - y = 62}$ ${y = 13}$ Therefore, the larger number is $75$, and the smaller number is $13$.